Conformally embedded spacetimes and the space of null geodesics

Abstract

It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of causally simple spacetimes into globally hyperbolic ones irrespective of curvature conditions. Examples of causally simple spacetimes are given not conformally embeddable into globally hyperbolic ones.

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Cited by in corpus (5)

• Globally hyperbolic spacetimes can be defined without the 'causal' condition
• A note on causality conditions on covering spacetimes
• Non existence of closed and bounded null geodesics in Kerr spacetimes
• Causal simplicity and (maximal) null pseudoconvexity
• On the space of null geodesics of a spacetime: the compact case, Engel geometry and retrievability